Progress in Mathematics

New Horizons in pro-p Groups

Editors: Sautoy, Marcus du, Segal, Dan, Shalev, Aner (Eds.)

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About this book

A pro-p group is the inverse limit of some system of finite p-groups, that is, of groups of prime-power order where the prime - conventionally denoted p - is fixed. Thus from one point of view, to study a pro-p group is the same as studying an infinite family of finite groups; but a pro-p group is also a compact topological group, and the compactness works its usual magic to bring 'infinite' problems down to manageable proportions. The p-adic integers appeared about a century ago, but the systematic study of pro-p groups in general is a fairly recent development. Although much has been dis­ covered, many avenues remain to be explored; the purpose of this book is to present a coherent account of the considerable achievements of the last several years, and to point the way forward. Thus our aim is both to stimulate research and to provide the comprehensive background on which that research must be based. The chapters cover a wide range. In order to ensure the most authoritative account, we have arranged for each chapter to be written by a leading contributor (or contributors) to the topic in question. Pro-p groups appear in several different, though sometimes overlapping, contexts.

Table of contents (12 chapters)

  • Lie Methods in the Theory of pro-p Groups

    Shalev, Aner

    Pages 1-54

  • On the Classification of p-groups and pro-p Groups

    Leedham-Green, C. R. (et al.)

    Pages 55-74

  • Pro-p Trees and Applications

    Ribes, Luis (et al.)

    Pages 75-119

  • Just Infinite Branch Groups

    Grigorchuk, R. I.

    Pages 121-179

  • On Just Infinite Abstract and Profinite Groups

    Wilson, John S.

    Pages 181-203

Buy this book

eBook £106.00
price for United Kingdom (gross)
  • ISBN 978-1-4612-1380-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover £133.00
price for United Kingdom (gross)
  • ISBN 978-0-8176-4171-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover £133.00
price for United Kingdom (gross)
  • ISBN 978-1-4612-7122-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
New Horizons in pro-p Groups
Editors
  • Marcus du Sautoy
  • Dan Segal
  • Aner Shalev
Series Title
Progress in Mathematics
Series Volume
184
Copyright
2000
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-1380-2
DOI
10.1007/978-1-4612-1380-2
Hardcover ISBN
978-0-8176-4171-9
Softcover ISBN
978-1-4612-7122-2
Series ISSN
0743-1643
Edition Number
1
Number of Pages
XIII, 426
Topics